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SUMMARY:Aggregation of bacteria by chemotaxis: mathematical and numerical 
 analysis - Nicolas Vauchelet (Univ. Paris 13)
DTSTART:20161124T140000Z
DTEND:20161124T150000Z
UID:TALK69275@talks.cam.ac.uk
CONTACT:Ariane Trescases
DESCRIPTION:Chemotaxis is the phenomenon by which cells direct their motio
 n according to a chemical present in their environment. In the case of pos
 itive chemotaxis\, strong aggregation may occur that create patch. From a 
 mathematical point of view\, it leads to the study of the so-called aggreg
 ation equation which describes the interaction through a potential. Such m
 odel can be derived thanks to a hyperbolic limit of kinetic equations mode
 ling the run-and-tumble process of bacteria. In this case the interacting 
 potential is pointy\, then solutions of aggregation equation may blow-up i
 n finite time. In this work\, we propose to study the existence of weak me
 asure solutions for such aggregation equation\, which allows to define sol
 utions beyond the blow-up time. Our approach is based on the definition of
  weak measure solutions for transport equation with discontinuous coeffici
 ents. Then we investigate its numerical simulations and propose a numerica
 l analysis.
LOCATION:CMS\, MR5
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